Related papers: Normal Binary Hierarchical Models
In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…
We present a quantitative basis-independent analysis of combinatory logic. Using a general argument regarding plane binary trees with labelled leaves, we generalise the results of David et al. and Bendkowski et al. to all Turing-complete…
We study the geometric structure of the statistical models for two-by-two contingency tables. One or two odds ratios are fixed and the corresponding models are shown to be a portion of a ruled quadratic surface or a segment. Some pointers…
The notion of regular cell complexes plays a central role in topological combinatorics because of its close relationship with posets. A generalization, called totally normal cellular stratified spaces, was introduced by the third author by…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by…
We introduce and study a family of simplicial complexes associated to an arbitrary finite root system and a nonnegative integer parameter m. For m=1, our construction specializes to the (simplicial) generalized associahedra or,…
We introduce a natural class of models of random chain complexes of real vector spaces that some classical ensembles of random matrices, the length $1$ case. We are interested here in the homological properties of these random complexes.…
Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…
Representations of vertex operator algebras define sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity conditions, we prove that such sheaves satisfy the…
For a given pair of numbers $(d,k)$, we establish the minimal number of vertices in pure $d$-dimensional simplicial complexes with non-trivial homology in dimension $k$. Furthermore, we solve the problem under the additional constraint of…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric…
Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukeherjee, and Boyer showed that…
We study the sequences of numbers corresponding to lambda terms of given sizes, where the size is this of lambda terms with de Bruijn indices in a very natural model where all the operators have size 1. For plain lambda terms, the sequence…
The theory of $N$-complexes is a generalization of both ordinary chain complexes and graded objects. Hence it yields deeper insight in the structure of these and offers a broader range of applications. This work generalizes the tensor…
We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some…
We provide first a categorical exploration of, and then completion of the mapping of the relationships among, three fundamental perspectives on binary relations: as the incidence matrices of hypergraphs, as the formal contexts of concept…
We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…
This paper serves as a first foray on regularisation for planar vector fields. Motivated by singularities in celestial mechanics, the block regularisation of a generic class of degenerate singularities is studied. The paper is concerned…